Much of the brain, perhaps 25-40% of it, is devoted to vision, and yet we understand little of it. Here we concentrate on the intermediate stages of visual processing that are lower than the conscious perception of objects and scenes but higher than retinal pointwise processing (roughly cortical areas V1 through V4/MT). There is widespread agreement that one important process at this intermediate level is a set of multiple channels or analyzers selectively sensitive to orientation, spatial frequency, spatial position, direction of motion, etc, the physiological substrate for which is probably the neurons of VIN2. Two different kinds of nonlinearity have also been proposed, by us and by others, as important processes at the intermediate level: (i) A spatial nonlinearity may result from complex second-order channels, which contain two stages of linear filtering with a rectification in between. (ii) The intensive nonlinearities of concern here depend on the visual pattern's contrast and operate in a general sense as contrast-gain-controlling processes. One such process is intracortical inhibition acting in a normalization network. Other possibilities include synaptic depression, facilitatory or inhibitory long-range interactions within a cortical area, and feedback from higher areas to lower areas. This proposal continues behavioral investigation of the two kinds of nonlinearity as they function in human visual perception. Some further work is proposed on the spatial nonlinearity, in particular on whether the complex channels' outputs are probabilistically independent and labeled as they go upstream. This proposal concentrates, however, on characterizing the contrast-gain-controlling processes that constitute the intensive nonlinearity. We propose a new line of psychophysical investigation into the dynamics of these processes. This investigation builds on an experimental paradigm -- the temporal Probe-Sine paradigm -- that has already proved of great use in characterizing retinal light adaptation, a luminance-gain-controlling process. The Probe-Sine paradigm will be used here in psychophysical studies of texture segregation and of sinewave-grating masking, studies designed to look at different possible contrast-gain-controlling processes. Predictions from models of possible contrast-gain-controlling processes will be used to guide interpretation of the empirical psychophysical results. Understanding the dynamics can help us both to distinguish among different processes and to understand their perceptual functions.